Week 4: Precalculus 11

Posted on February 22, 2019 by paigep2016

This week in precalculus I learned how to add and subtract radicals together.

Firstly, we need to know what a radical is. A radical is pertaining (related) to or forming a root. An example is, $\sqrt {4}$ .

Radicals can come in two forms: a mixed radical, 2 $\sqrt {2}$ , or an entire radical, $\sqrt {64}$ . Radicals always include a root sign and a radicand. Some radicals also may include variables, $\sqrt {6x}$ .

To add radicals together whether they are mixed or entire radicals the radicand must be the same. The radicand is the number (or it may be a variable) that is under the root sign. To get the radicands the same you may have to use prime factorization to simplify one or both radicals.

Once the radicand is the same you add the coefficients of the radicals together and leave the radicands the same, as they are the same. All radicals have coefficients. Coefficients are the numbers to the left outside of the root sign. Although some radicals may not have an overt coefficient there is always a coefficient of one.

Finally, you add or subtract all the coefficients together and leave the radicand the same and you have your sum.

Week 3: Precalculus 11

Posted on February 14, 2019 by paigep2016

Absolute Value’s

This week in math we learned what absolute value is.

The absolute value is indicated by two vertical bars “| |”. These bars are grouping symbols and are similar to brackets but do not serve the same job. Similar to brackets you have to solve everything between the bars “| |” before continuing to solve the problem but, unlike brackets these bars do not indicate multiplying, which some people get confused by.

Absolute value is the distance from 0. So that means the absolute value is never negative. |-3| = 3, because, on a number line if you were at zero and went three to the right is it is the same distance as if you were to go to the left. Below is a number line representing my explanation:

At first, absolute value confused me but after learning the basics it is really quite a simple aspect and easy one.

Week 2: Precalculus 11

Posted on February 10, 2019 by paigep2016

Geometric Sequences

This week in math I learned what a geometric sequence is.

A geometric sequence is a set of terms (numbers) that multiply by the same number each time. This is called the common ratio. To determine what the common ratio is, you have to take $t_n$ and divide it by $t_n$ .

When you have a geometric sequence and need to find $t_n$ there is a simple way we could do that.

If my geometric sequence was 2, 4, 8, 16, 32… and I wanted to find $t_6$ , I would take $t_5$ and divide it by $t_4$ . In this case, the unknown term isn’t far from $t_5$ so this way would work, otherwise, you would have to use a formula to determine a further term. In this equation, the common ratio would be 2.

So, to find $t_6$ would take 32 ( $t_5$ ) and multiply it by 2. $t_6$ is equal to 64.

Week 1: Precalculus 11

Posted on February 4, 2019 by paigep2016

Arithmetic Sequences

This week in math we got introduced to arithmetic sequences.

An arithmetic sequence is a sequence of numbers that increases or decreases by the same amount every time. You also may know arithmetic sequences are very similar to linear equations.

Arithmetic sequences may have 4 terms or 400. A formula has been created so when you need to know what term 365 is you don’t have to write out 365 terms.

Below is an example when trying to find the 26th term:

(won’t allow me to upload any document or picture/screenshot right now, I have a picture if you would like to see my understanding)